Is there any benefit in using a continuous integration job (e.g. hudson) to publish the method configuration, rather than manually publishing the configuration using the EPF user interface (Configuration > Publish)?

I think there is. I always recommend (also) an automated publish. Of course you can do that with for example with a Cron job. Using such a job you could for example do a daily publish of the latest and greatest from the version management system. But Jenkins offers a lot more than a Cron job. You can schedule to publish daily but you can also always easily start the job manually using the Jenkins web interface. Also you have the benefit of being able to see console log of the last job and also previous jobs. You can send mails if something fails. There are many, many benefits.

There is a downside however. As far as I can tell there is no way to publish the search feature from the command line.